The All-Seeing Eye

Musings from the central tower…

Monopoly

The name of the game is Monopoly.  The object of the game is to win.  You win by having the most net worth at the end of the game or by being the last player left after all other players have gone bankrupt.

Basically, your goal is to collect money and property – as much as possible, by any means available.

Most people are probably familiar with Monopoly, which makes it a good example for a thought experiment.

Imagine that four friends are playing Monopoly and a fifth friend shows up and asks to get into the game even though some number of turns have already passed.  How can this fifth friend be integrated into the game?

One way is to start the person the way everyone else started: at Go, with $1500 and a pair of dice.  The beginning is the logical place to start, after all.  This method presents problems, though.  The four original players have had many turns to increase their wealth and their earning potential.  Many good properties have already been bought.  Monopolies may have already been established.  Depending on how late in the game it is, this fifth player may be at some great disadvantage.  Imagine if 90% of the properties on the board are already owned.  The fifth player has virtually no chance of winning – of surviving on the board – under these circumstances.

Another way is to grant the person some portion of the money/property on the board.  You could total the value of the properties each player owns, average the totals, and then randomly assign the new player  unowned properties until that average is approximated.  You could do the same for money.  However, if there isn’t enough unowned property to do this, you’d have to take property away from some of the players who are already playing.  How can this be done fairly?  Should the property be taken from the winning player(s), or equally from all?

Another way is to simply restart the game.  This isn’t necessarily fair to the players who were doing well – their good luck and good strategy ends up going unrewarded.  However, the player(s) who think(s) he/she/they would have won can at least declare victory in this case.  I have found that generally speaking
this is the most oft-chosen option for inserting a new player into an existing game, for the simple reason that usually at least half of the players are not winning and usually the choice of methods comes down to a loosely democratic vote:  All of the players who are losing choose to restart.

Aside from the highly practical use that this line of thinking has in actually inserting new players into existing games – a situation I have encountered in life from time to time – we can also consider the larger implications, like when we insert new players into the more realistic economic systems presented by, for instance, the economy.  Imagine, for instance, that half the population of some country was playing some game analogous to Monopoly – attempting to acquire money and property and personal enrichment – for years, or decades, or centuries.  Imagine then that the other half demanded to be inserted into the game.  How would we fairly insert these newcomers?

Obviously this question is not simply theoretical.  Various large population groups have been granted property rights in our history – women, for instance, and blacks – rights which amount to $1500 and a pewter thimble.  These groups were then allowed to compete freely with the people who already owned almost all of the property, people who were busily going through the Monopoly winning strategies of bankrupting whoever they could and consolidating and developing their assets.

Just letting someone into the game doesn’t establish fairness.  These groups weren’t really given a chance.  Even those who did start off with some property – many former slaves were given land during Reconstruction, and women could always inherit an estate from a husband or father – were still at a disadvantage.  Imagine starting a game of Monopoly with a house on Baltic Avenue when another player has hotels on Boardwalk and Park Place.

In the game of the American economy, women, blacks, and immigrant groups have had to claw their way up from the bottom with the help of luck, charity, and government aid.  It’s no wonder that the players who are already winning want to deny entry to immigrants, why they fought to keep women from having the right to own property.  It’s no wonder that the players who aren’t doing so well want to restart the game and distribute everything evenly.  But when we assess some data – the wage gap between men and women, for instance – it’s important to keep in mind that some of the players started late.  If women owned half the property and controlled half the wealth in the American economy, would there still be a wage gap?

And before we say that some group has had enough opportunity to improve their lot, let’s ask ourselves how many turns we would need before we caught up in a game of Monopoly if we started fifty turns late.

Again, no solution presents itself.  What is fairness?  How can all players be satisfied with a solution?  Certainly whatever happens, it will require the cooperation of people who don’t currently acknowledge that there is a significant problem with how the game was set up in the first place.

June 4, 2008 Posted by | Economics, Feminism, Game Theory | , , , | 3 Comments

The Prisoner’s Dilemma: A Semiotic Analysis

One of the many fascinating aspects of the Prisoner’s Dilemma is the way that it is framed. Take, for instance, this concise description from the Stanford Encyclopedia of Philosophy:

Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. “You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I’ll see to it that you both get early parole. If you both remain silent, I’ll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.”

First of all, what’s in a name? “The Prisoner’s Dilemma” tells us about a dilemma faced by a prisoner – note the placement of the apostrophe. In this example, though, there are two prisoners, and they both face the same dilemma. Why, then, do we not see this dilemma called “The Prisoners’ Dilemma?”

Well, the dilemma only comes about as a result of the separation of the two prisoners into individuals. If there were one player controlling both prisoners and trying to maximize her score, she’d have no dilemma. The Prisoner’s Dilemma, however, is faced by one individual, alone, isolated from contact with her fellow prisoner.

That leads to another question: why a prisoner? There are plenty of ways to propose the same paradigm – for example, two students who turned in identical examinations. Or an invading army offering a reward for whoever will open the town’s gates at midnight. The point is there are any number of anecdotes that match the payoff matrix of the PD, and perhaps infinitely many could be invented. Prisoners were chosen – why?

On some level, the prisoner’s dilemma applied to prisoners is well-understood. Plenty of people enjoy the legal drama as a story – plenty of people have been exposed, in our time, to Law and Order, Homicide, or CSI, and these modern shows have predecessors, and those predecessors use tropes set up in literature.

I would argue, however, that the choice of prisoners goes deeper than a simple familiarity. There is a match in situation between a prisoner and one caught in the prisoner’s dilemma. In other words, if this same problem were explained using students caught cheating instead of criminals caught robbing a bank, the students would still feel trapped. They would still feel like prisoners. And the person who reads the dilemma sympathizes with the subjects of the dilemma and feels their sense of being trapped. The situation that we call the Prisoner’s Dilemma works because of panoptic power, and panoptic power makes its subjects into prisoners, much more than it makes them into students, or frightened villagers.

When I say that people sympathize with the subjects of the dilemma, I mean, the reaction intended by the framing of the dilemma is that the reader puts herself in the place of the prisoner. The reader must ask “What would I do if offered such a deal,” and not “What would I do if I were the prosecutor and I had two prisoners?”

And that brings up another quite interesting point. We are told explicitly what the preferences of the prisoners are: they want to maximize their freedom, even to the detriment of their partner in crime. We are never told the goal of the prosecutor, although the prosecutor’s actions seem to speak for themselves. The prosecutor’s goal is, simply, to get convictions – to maximize jail time for the two prisoners. In our legal system, prosecutors build their careers by putting people in jail. If the goal of the prosecutor were to find out the truth, the Prisoner’s Dilemma would not be an effective tool. Imagine that one prisoner committed a crime and the other prisoner just happened to be in the wrong place at the wrong time. Who would be more likely to confess a crime, thus putting the other person in jail, and who would be more likely to maintain her innocence, thus going to jail?

If the panoptic model helps to maximize power, and the Prisoner’s Dilemma uses the panoptic model on behalf of authority, then it is a blind authority whose power is maximized. The authority does not care about the well-being of the society it has authority over; it is merely concerned with maintaining its own power. And indeed, this relationship is reflected by the names of the moves in the Prisoner’s Dilemma: defect and cooperate.

To defect is to cooperate with the authorities. To cooperate is to be defective from the point of view of the authority – a defective, criminal citizen, a defector, a saboteur of civil authority. The terms “defect” and “cooperate” refer to a presumed partnership between the two prisoners. I say presumed because nowhere in the description of the Dilemma is it stated or implied that the two prisoners have made any kind of agreement about how to handle such an eventuality as being placed into the Dilemma. The two prisoners are presumed to be partners only in the sense of (allegedly) participating in a criminal activity together; since nothing is stated about their guilt or innocence it may well be that neither of them has even met the other. The two are described as “accomplices,” but accomplices who prioritize each other’s well-being much lower than their own – in other words, hardly friends, or compatriots, or long-term partners in any sense.

However, the term “defect” implies something defected from, some country or alliance. Again, the term cooperate is ambiguous – the prisoners can cooperate with each other or with the authorities. We’ve already established that the authorities do not have the best interests of the prisoners in mind, and now we also establish that if the prisoners are to do any cooperating, it will be with each other, against the authorities. The authorities want to gain power by destroying the bonds of cooperation and causing someone to defect from society; the prisoners want to remain free by holding together as a society.

The choices could have been named differently. Confession could have been called cooperation – and certainly if we view the game from the perspective of the prosecutor, a confession would be a way for a prisoner to cooperate. However, again, the PD puts us in the place of the Prisoner, who is depicted as being in society with other prisoners but not with the prosecutor or the authorities.

Again, the PD does not have to be expressed in these terms that suggest that authority is opposed to, rather than part of, society. It doesn’t have to, but it is, and I consider this highly significant. The PD is not a dilemma about how we get justice – it is a dilemma about how we get freedom. And the freedom of the reduced sentences is not simply a freedom from jail, but a freedom from the power that would turn us against each other in pursuit of its own anti-social goals.

March 9, 2008 Posted by | Game Theory, Power | , , , | Leave a comment

The Prisoner’s Dilemma and the Panopticon

I’ll start this post with a brief recap:

The Prisoner’s Dilemma (PD) is a concept in game theory that describes the situation of two suspects who have been apprehended by the authorities. In the PD, the authorities need a confession in order to get the conviction they want, so they come up with a scenario to try to convince each suspect to confess. They offer each prisoner a reduced sentence in exchange for a confession that incriminates the other prisoner. If both prisoners stay silent – a play that is conventionally called “cooperate” – they both get a short sentence. If one prisoner chooses to “cooperate” but the other prisoner makes a confession – a play called “defect” – the defector goes free and the cooperator gets a full, long sentence. If both “defect” they both get a medium sentence.

Like the Traveler’s Dilemma, it is better in the Prisoner’s Dilemma for both players to cooperate – choosing (100) or choosing to stay silent. Also like the TD, in the PD if one player cooperates, the other player can increase his payoff by defecting – choosing (99), or choosing to confess. And finally, if one player defects – by choosing (2), or confessing – the other player can mitigate the harm done by also defecting.

The Panopticon is a philosophical concept that describes the situation of prisoners in a more general sense. The original panopticon was a design for a physical structure that would house prisoners in such a way as to maximize the number of inmates who could be supervised by one warden. This design consisted of a central tower where an observer could remain unseen by the inmates but from which all of the inmates could be seen. The inmates were situated in individual cells surrounding the central tower, separate from each other.

The idea of the panopticon is that this situation – isolation and the perpetual possibility of surveillance, would produce within each prisoner a sort of self-surveillance. Each prisoner would know at all times that he could be under supervision, and so each prisoner will act at all times as though he were under supervision.

The difference between self-surveillance and regular surveillance, though, is that self-surveillance can be much more intrusive. After all, an outside observer can only see certain physical manifestations of our actions – in other words, can only see what our actions look like. We, on the other hand, can, in a sense, see what our actions are. We form the intent that turns a motion into a gesture, an activity into an action, a sound into a word. We can read our own minds.

This paves the way for what I like to call the panoptic model of power. The panoptic model of power says that power is constituted and magnified by the effects of isolation and self-surveillance. Isolation and self-surveillance are interlocking, mutually reinforcing forces – in other words, isolation helps constitute self-surveillance and self-surveillance helps constitute isolation. A good example of how this works is the Prisoner’s Dilemma.

The most obvious intersection of the PD and the panoptic model of power is isolation. Without isolation, the PD would not be a dilemma. Imagine the PD with both prisoners in the same room. They can talk to each other, they can see each other, and they know what the other one is doing at all times. In other words, you’ve removed the hope that one player can defect without the other player defecting, and so now the options are only (defect, defect) or (cooperate, cooperate). Between those two options, one is strictly better, and it’s the one that benefits both players the most – so there’s no dilemma.

The self-surveillance part of the PD may not be as obvious. First we can look at the effects: The expected effect of the PD is that both prisoners confess. Is not confession a form of self-surveillance? It’s self-incrimination, certainly. One might expect the prisoners to provide additional information to the authorities in the course of their confession – details of the crime, perhaps the location of weapons used in the crime, perhaps details about other accomplices, or motives, or planning. In other words, the PD goes a lot deeper than the surveillance the authorities were able to place upon the prisoners without the PD.

To find the cause, we need only locate the central observer. In the panopticon, the prisoner exercises self-surveillance because the prisoner might be under surveillance. In the PD, the prisoner confesses because the other prisoner might confess. In the panopticon, the possibility of being watched leads the prisoner to watch himself. In the PD, the possibility of being incriminated leads the prisoner to incriminate himself.

The Prisoner’s Dilemma, thus, provides both an example of the panoptic model of power at work, and an insight into one of the mechanisms of the panoptic model of power.

February 17, 2008 Posted by | Game Theory, Power | , , , , , , | 2 Comments

Free Will, Determinism, and Motivation

It is possible to look at the universe like a giant computer. If you know the software a computer is running and all of its inputs you can predict the result. Similarly, one might think that if you knew all the rules of the universe – that is, if you understood physics perfectly and accurately – and if you knew the position and velocity of each particle in the universe, you would be able to predict the results – that is, how everything would turn out. Such a view is called determinism. When Newton first proposed that all matter obeyed certain laws, he was accused of atheism, because the obvious implication of his theories was determinism, which is a theory that leaves no place for God and no place for free will.

The question of free will vs. predestination or determinism is, of course, older than Newtonian physics, but physics is the way in which I first conceived of the question. One might ask, if God is all powerful, how can anyone act in a way God does not want? One might ask, if God knows all, then isn’t destiny written – isn’t there no way to change things? I have never been particularly into theology, but physics always fascinated and frightened me.

Some time ago I read Isaac Asimov‘s Foundation trilogy, which despite its name consisted of approximately thirteen thousand books. This series is based upon the idea that there was a mathematician named Hari Seldon who was able to predict the course of history using mathematical models and a deep understanding of historical trends. I did not find this idea credible. People, after all, are far too complicated to reduce to a mathematical model. Aren’t they?

Can we predict what people will do in a given situation? If we can, what does that say about free will? If we can’t, how can we enact social change?

In Freakonomics, authors Levitt and Dubner describe a scenario in which parents were charged a small fee (I think it was $3) for being late to pick their children up from daycare. The result of this fee was that lateness increased dramatically. According to Levitt and Dubner, the fee was too low, and parents felt as though paying $3 justified their lateness. In other words, when no provision is made for lateness, the parents have to pick their kids up on time or risk their kids being scared and alone. When the daycare center charges for lateness, watching the kids for a few more minutes becomes just another service that the parent can buy, and buy they do. The point of this story is that incentives don’t necessarily work the way we think they will. There are complicated issues at stake even in something as simple as daycare. As we saw in the Traveler’s Dilemma, it’s not a simple task to predict how people will make their decisions, and sometimes rational behavior isn’t what theorists think is rational.

However, what both of these scenarios show is that despite the difficulty, despite the complications, it is possible to develop models and predictions for how people will behave. It is possible to find, with experimentation, the fee amount at which parents will begin picking their children up on time to avoid the fee. It is possible to find, with experimentation, the punishment amount at which people will begin picking the low number rather than the high number in the Traveler’s Dilemma. In other words, people’s behavior may be more complicated than we think, but it is not unreasonable. People act based on motivations, and although these motivations are often not obvious, they are there and they can be found.

Of course there will always be exceptions. There’s always room for free will. There will always be people on the far ends of the bell curve, people who defy expectations and act inexplicably. But in order to effect positive change in the world, we have to believe that we can predict behaviors for most people. We have to believe that there’s a number of dollars that will decrease the amount of late pickups from daycare. After all, isn’t this how we determine prison sentences? Isn’t there a number of years of incarceration that we believe will make the commission of murder unattractive to most potential criminals? Isn’t there a number of dollars that we believe will deter people from speeding and thus decrease the number of traffic accident fatalities?

I’ve never really believed in free will. I’ve always thought that everything is already determined by particle vectors, that everything I do is explainable by something that happened to me in childhood or by a set of circumstances that outlined my choice to such an extent that I didn’t really have a choice. And that’s why, for me, I think it is important for us to search for these motivations, search for these incentives, to build and discredit and rebuild these mathematical models to predict behavior. Because I want to set things up so that people have no choice but to make the right choices. I want a society full of people who pick 100 on the Traveler’s dilemma and pick their children up on time from daycare, and if we’re going to have that we have to pick the right game.

And that, in turn, is why it’s worth looking at something like the Traveler’s Dilemma and finding out that people will cooperate with each other as long as the risk for doing so isn’t too high. It’s why it’s worth looking at the daycare paradox to find out how much guilt is worth. It’s why it’s worth asking why people follow their king or their president against their best interests. We need to find out what motivates people. And in exploring incentives and economics, game theory and modeling, philosophy and psychoanalysis, that’s exactly what I hope to do. I hope to find a solution, a way to set up society so that we’re all playing a game that everyone can win.

In closing, right now I feel that most people are not playing a game that everyone can win. There’s a game called the Prisoner’s Dilemma. In this game, two prisoners are in the custody of law enforcement, but the police don’t have enough evidence to convict them of a serious crime. Each of them is told that they are both suspects and given the following options. If one prisoner gives up the other, that prisoner will go free and the other will go to jail for a long time. If neither of them confesses they will both serve a short sentence for whatever smaller crimes the police can put on them. If they both confess they’ll both serve a short sentence. The implications of the game are that it is better for each player, no matter what the other player does, to confess their crime. Unlike the Traveler’s Dilemma, the Prisoner’s Dilemma tends to lead to uncooperative behavior – in other words, it is much better for each player to screw the other player over, unlike in the TD in which screwing the other player leads to a greater loss.

The Prisoner’s Dilemma game describes many situations in modern life – situations in which people have a great incentive to hurt other people. If there is some way to change the rules of the game so that, like in the Traveler’s Dilemma, or many other games, people have an incentive to help other people, then everyone could benefit immensely. Changing the rules of the game is what I’m aiming for, but it’s going to take a lot of searching to find the right game and a lot of convincing to get people to play it.

February 10, 2008 Posted by | About, Economics, Game Theory | , , , , , , , , | 2 Comments

Traveler’s Dilemma and Opportunity Cost

As a followup to my last post, I thought now would be a good time to say some things about opportunity cost, or The OC.  Please do not confuse this with any other things called The OC.

Opportunity Cost is an economic analytical tool – a measure of the cost of a missed opportunity.  It goes like this.  Let’s say you have a dollar and you’re standing on the street at a hot dog cart.  The cart is selling pretzels for $1 and hot dogs for $1.  If you buy the hot dog, you can’t buy the pretzel.  Therefore the opportunity cost of buying the hot dog is one pretzel.  Conversely if you buy the pretzel you can’t buy the hot dog.  So the opportunity cost of the pretzel is one hot dog.  Simple, right?  At first glance this seems a trivial and reductive measure for an economist to be thinking about, but in real life, when applied to more complex situations, we can see the value of considering the opportunity cost.

Let’s try another example.  You have a dollar but you aren’t hungry, and you’ve got a year.  You can keep the dollar in your pocket and at the end of the year you’ll have a dollar.  Or you can put the dollar in a bank and at the end of the year you’ll have, let’s say, $1.05.  The average person would think that if they kept the dollar in their pocket, they haven’t lost anything, and in one sense this is true.  However, they have missed something – the opportunity to earn $.05.  The opportunity cost of holding onto the dollar was five cents.  Doesn’t seem like much, but what if it’s a thousand dollars?  A million?

The point is, when there’s money at stake it pays to consider the opportunities that you have when making choices, because in some sense, missing the opportunity to earn money is sort of like losing money, even if it’s money you never actually had.  An opportunity is worth something.  If you don’t believe me, play poker.  If you fold a hand, and it turns out at the end that you would have won if you had stayed in, you will feel like you have lost something.  What you’ve done is missed an opportunity, and the loss you’re feeling is the opportunity cost.  Folding may have been the right decision based on the odds, but you’ll still feel bad that you didn’t get the pot.

So what does opportunity cost have to do with the Traveler’s Dilemma?  Well, it’s another way of evaluating possible plays in the TD, and it demonstrates a major flaw in the models used by game theorists to “solve” the TD.

To recap, in the TD, game theory says that logically speaking, a player ought to play (2).  Many people intuitively feel that they should play higher, and (100) is perhaps the most common play, with (95) to (100) comprising the majority of plays in some experiments.  According to Kaushik Basu, (2) is the correct or best play, because of a game theory concept known as the Nash Equilibrium.  Further, (100) is the worst play, because it is the only play in the game that is “beaten” by every other play.  In other words, if player 1 plays (100) and player 2 plays anything else, player 2 will be rewarded more points than player 1.  If this logic is to be believed, (2) is a better play than (100), and people, if they are acting “rationally,” ought to play it.

But let’s look at the OC to see if that’s true.  Let’s say player 1 plays (100) and player 2 plays (2).  The rewards, then, are 0 points to player 1 and 4 points to player 2.  However, given player 2’s play of (2), the highest score player 1 could possibly have acheived by making a different play is 2, by playing (2).  Any play other than (2) results in a score of 0.  So, player 1 lost 2 points by not playing (2), or, to put it another way, his opportunity cost for playing (100) was 2 points.

Player 2, however, is in a much worse situation.  He played (2) and got 4 points.  Given player 1’s play of (100), the highest score possible for player 2 was 101, with a play of (99).  In other words, by playing differently player 2 could have gotten 101 points, but instead he got four.  That means that his opportunity cost for playing (2) was 97 points.

So, in the above example, on the face of it it seems like player 2 won – he got 4 points, while player 1 got none.  However, if you look at it a different way, player 2 lost 97 points while player 1 only lost 2.  If you consider the scale of a loss of 2 vs. a loss of 97, you see that a play of (100) is much less risky than a play of (2).

In fact, for an opponent’s play of 2, the OC of (100) is 2.  For any number between (3) and (99), the OC is 3.  And for (100), the OC of (100) is 1.  The OC of (2), however, is (Opponent’s play – 3).  That means that for any play above (6), the opportunity cost of (2) is higher than that of the opponent’s play.

So the (2) player almost always loses more money than his opponent – not that the players are losing money that they actually possessed, but money that they could have – and perhaps should have – earned.  If you ask any economist or poker player, that loss can sting just as much as a loss of cold hard cash.

The thing is, if you evaluate the Traveler’s Dilemma in terms of Opportunity Cost, the definition of improving one’s position changes, and therefore so does the Nash equilibirum.  It’s a situation where gaining money and not losing opportunity are not the same thing – and this situation probably comes up fairly often in the real economy, which is why opportunity cost is important as an economic concept.  Rational choices and selfishness, therefore, cannot necessarily be evaluated successfully using only the rubric of amassing the most gain by the end of the game.  There are other measures of success, and people do use them.  Game theorists and economists alike would do well to remember that.

January 25, 2008 Posted by | Economics, Game Theory | , , , , | 1 Comment

The Traveler’s Dilemma

Now for some real content. I came across this article in Scientific American about the Traveler’s Dilemma. To explain briefly, the TD is a game in which two players are each asked to select a number within certain boundaries (2 and 100, in the example). If both players select the same number, they are rewarded that number of points. (In the example, each point is worth $1, which makes the game of more than academic interest.) If one player’s number is lower, they are each awarded points equal to the lower number, modified by a reward for the player who selected the lower number and a penalty for the player who selected the higher number. So, for instance, if you choose (48) and I choose (64), you get 50 points and I get 46 points.

The intuition that I had upon reading the rules of this game was that it would be “best” for both players to choose (100). That is certainly true from a utilitarian point of view: (100, 100) results in the highest total number of points being given out – 200. The runners up are (99, 99), (100, 99), and (99, 100) with 198. However, there are two small problems – here’s the dilemma part – that prevent (100, 100) from being the “best” choice: one, the players are not allowed to communicate, and two, the (100, 99) and (99, 100) plays result in one player receiving 101 points – an improvement, for that player, over a 100 point reward.

So, the reasoning goes, if player one predicts that her opponent will play (100), she should play (99) in order to catch the 101 point reward. Her opponent, however, ought to use this same strategy, and also play (99), in which case player one ought to play (98) in order to trump her opponent, and so on and so forth. This reasoning degenerates to a play of the minimum number – in the example, (2). According to Basu, the author of the article, “Virtually all models used by game theorists predict this outcome for TD.”

However, reality does not follow these models. When people are asked to play the TD, many of them choose 100. Many of them choose other high numbers. Some seem to choose at random. Very few choose the “correct” solution – (2) – predicted by game theory. Something’s up.

Basu takes this to mean that all of our assumptions about rational behavior need to be questioned. With my philosophical background, I happen to have different assumptions about rational behavior than the mainstream, and so for me the results of the TD are not surprising in any way. But perhaps the best way to explain why the results to not surprise me is that I am a gambling man. Continue reading

January 24, 2008 Posted by | Economics, Game Theory | , , , , , , , , , , , | 6 Comments